A satellite in geostationary orbit transmits a periodic signal that serves as a synchronization beacon for ground stations. The signal alternates between a value of 2 volts for the first half of the period and -2 volts for the second half. As a signal processing specialist, determine the DC component of this signal, which is crucial for maintaining synchronization.

(a)  

A satellite transmits a signal x[n] = {1, 3, 2} to a ground station, which uses a filter with an impulse response h[n] = {1, 2, 1} to process the received signal. The ground station needs to determine the output signal to evaluate the filter's performance. As the engineer in charge, compute the output signal y[n] after filtering the transmitted signal.

(a)  

During a deep space mission, your team receives a signal from a distant satellite, which can be modeled as x(t) = ( e^-3t ) u(t) , where u(t) is the unit step function. To analyze the signal for possible Doppler shifts and signal degradation, compute its Laplace Transform, which is essential for further analysis in the frequency domain.

(a)  

A satellite in orbit experiences a sudden impulse due to a solar storm, which causes a perturbation modeled by the differential equation ( d^2x(t) / dt^2 ) + 9 x(t) = δ (t) , where δ (t) represents the impulse. As part of the mission control team, you are tasked with determining the satellite's response x(t) to assess its stability post-perturbation. Solve this equation using the Fourier Transform.

(a)